To find the value of [tex]\( f(x) \)[/tex] when [tex]\( x = -4 \)[/tex], we need to determine which piece of the piecewise function to use based on the given value of [tex]\( x \)[/tex].
The piecewise function is defined as:
[tex]\[
f(x) = \begin{cases}
x^2 & \text{if } x \leq 3 \\
2x - 4 & \text{if } x > 3
\end{cases}
\][/tex]
Given [tex]\( x = -4 \)[/tex]:
1. We observe that [tex]\(-4 \leq 3\)[/tex].
2. Since [tex]\(-4\)[/tex] is less than or equal to [tex]\(3\)[/tex], we use the first part of the piecewise function, which is [tex]\( f(x) = x^2 \)[/tex].
Now, we substitute [tex]\( x = -4 \)[/tex] into this part of the function:
[tex]\[
f(-4) = (-4)^2
\][/tex]
Calculating the square of [tex]\(-4\)[/tex]:
[tex]\[
(-4)^2 = 16
\][/tex]
Thus:
[tex]\[
f(-4) = 16
\][/tex]
Therefore, the value of [tex]\( f(x) \)[/tex] when [tex]\( x = -4 \)[/tex] is [tex]\( \boxed{16} \)[/tex].
